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In this caseUnlike the common chord examples, both E and A are common tones we move directly between chords that are carried over, although E not diatonic to both keys - C Major does not contain the Am A chord , and vice versa for C E Major and lacks the A C chord. Yet the common E note between them bridges the gap particularly well, without creating a stark contrast between keys.
→Common Modulations
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* [[Music Theory - Diatonic Chord Progressions]]
* [[Circle of Fifths]]
== Notation ==
In terms of traditional musical notation or guitar-specific tablature, modulations aren't specifically notated. The non-diatonic notes for a certain key simply appear. For traditional notation, the key signature may change; however, this is typically reserved for the start of new section. Rather, you'd see more {{s}}, {{b}}, and {{natural}} signs appear next to notes. For guitar tab, there is no key signature - you would simply see notes used that were not used before that point in the song. Knowing that there is a key modulation is not necessary for the performance of particular piece; it is only necessary for understanding it in terms of theory.
In terms of harmonic analysis, modulations alter the roman numerals used to mark chords. For example, while C is the I chord of C Major, it is the III chord of A Minor. The key must be specified for this analysis to make sense, and sometimes there is overlap. For instance you may see:
'''Chords -''' C F G C Em Am D G
'''Analysis 1 -''' C: I IV V I iii vi
'''Analysis 2 -''' G: vi ii V I
You can see the "C:" and "G:" in the respective analysis lines indicating the key, with the following roman numerals outlining the member chord from that key. In this case there is overlap, where we may interpret the Em and Am chords as belonging to either key. In other cases where the point of modulation is unambiguous, you may see this condensed to a single line:
'''Chords -''' C F D G
'''Analysis -''' C: I IV G: V I
When discussing modulations ''outside of notation'', we can use an arrow, such as "=>" or "->" to indicate the modulation. For example, "C -> Am" (C Major to A Minor) or "C => G" (C Major to G Major).
If we want to make such modulations generic to any key by using roman numerals, this can get a bit more tricky. For example, if we want to discuss a modulation from a major key to a minor key whose tonic note is the 6th note of the major key, we could say "I -> vi". The uppercase "I" and lowercase "vi" indicate that the original key is major, but the new key is minor, and the "vi" also indicates the new key's tonic note is the 6th's note of the original major key. But what if the tonic note of the new key is non-diatonic to the original key? Then we have to use a {{b}} or {{s}} to indicate that. So moving from C -> A{{b}}m could be generically written as "I -> {{b}}vi". Cm -> A would be written "i -> {{s}}VI" - the 6th note of C Minor is A{{b}}, but we sharp it to get A.
We must use "I" or "i" to indicate the original key. "IV -> V" makes no sense - we are moving from the 4th note of ''what'' key? We are also bound to the common heptatonic major and natural minor scales. If the source or destination keys use other scales, they must be written out fully - "A modulation from lydian to the harmonic minor key built on its 4th note".
== Common Modulations ==
Modulations usually take place between highly-related keys (those with the most common notes). See the table below.
{|
|
{|class="wikitable"
!colspan="2"|
|-
| '''M7''' || 2 || 5 || 4
|}
|
{|class="wikitable"
!colspan="2"|
!colspan="3"| Key 2 Type<br>and number<br>of common<br>notes
|-
! Key 1 Type
! Key 2 Root's<br>relation to<br>Key 1 Root
! Major !! Minor !! Harmonic<br>Minor
|-
!rowspan="13"| Minor
|-
| M7 || 3 || 2 || 3
|}
|
{|class="wikitable"
!colspan="2"|
!colspan="3"| Key 2 Type<br>and number<br>of common<br>notes
|-
! Key 1 Type! Key 2 Root's<br>relation to<br>Key 1 Root! Major !! Minor !! Harmonic<br>Minor|-!rowspan="13"| Harmonic <br>Minor
|-
| '''U''' || 4 || '''6''' ||
|-
| '''M7''' || 3 || 3 || 3
|}
|
|}
=== Common Tone ===
A note common to the source and destination key is sustained during the transition. For example, a C -> E modulation could sustain the A E in the vi I chord of C (Am) while moving to the IV chord of E (A), which also contains AE.
C Am F G C A B7 E C: I vi IV V I E: IV V7 I E--0----1----3----0----0----0-----2-----0-- B--1----1----3----1---(x)---2-----0-----0-- G--0----2-2---0----0-2--(x)---2----2----1-- D--2----3----0----2---(x)---2-----1-----2-- A--3----3----2---0-3---(x)---0-----2-----2-- E-------1----3------------------------0--
While this example has somewhat-related keys, this modulation method can link virtually any two keys, as it's basically guaranteed that any two keys will share at least one common note.
Useful for modulating between two keys that are not closely related, chromatic modulation uses a chromatic line to bridge the keys. In other words, for the chords chosen, one voice can move up or down 2 or more half-steps. This necessarily implies the transition will occur over at least 3 chords. For the strongest effect, the chromatic line should lead into the root of the new key.
For example, consider a modulation from C Major to A Harmonic Minor. C Major has a G note, while A Harmonic Minor has G{{s}} and A. This allows us to create a G - G{{s}} - A chromatic line through the following progression: G - E - A. That's ('''G''' B D) - (E '''G{{s}}''' B) - ('''A''' C E). If we follow good [[Voice Leading|voice leading]], we can keep the G, G{{s}}, and A notes in the same voice, thus getting the chromatic line. G is the V chord of C Major. E is the V chord of A Harmonic Minor. The progression could be written as:
C F G E Am C F G E Am C: I IV V C: I IV V Ahm: V i Ahm: V i E--0----1----3----0----0-- E-------------------0------ B--01----1----0----0----1-- B------------------------- '''G--0----2--**0----1----2** G--0----2--**0----1----'''2** D--2----3----0----2----2-- D--2----3----0----2----2-- A--23----3----2----2----0-- A--3----3----2----2----0-- E-------1----3----0----0--- E-------1----3----0-------
<small>''Notice the chromatic line on the G string.''</small>
Here's another example, modulating from C to G, using a chromatic run on the high E string. Notice how seamless this sounds, especially with the chromatic line as the highest-pitched voice (soprano).
C F D G
C: I IV
G: V I
E--**0----1----2----3**
B----1----1----3----3--
G----0----2----2----0--
D----2----3----0----0--
A----3--------------2--
E-------------------3--
Depending on the keys used, it may be more difficult to achieve the chromatic line with only the diatonic chords of the two keys. In these cases, we can resort to using a [[Borrowing Chords/Notes#Secondary Dominant|secondary dominant]] or some other non-diatonic chord.
A phrase modulation avoids any transition whatsoever, occurring abruptly between two virtually independent phrases. The first phrase in the original key will end on a cadence, finding resolution and ending. The next phrase begins in the new key, with no harmonic or melodic bridge to ease the transition. This modulation is commonly between closely-related keys, preventing a completely disjointed feel. However, the transition is typically quite noticeable, which is the point of this modulation method.
A E A E G#D Em A:I V I ED:I iii ii E-------------------------|----------------...--- B-------------------------|----------------...--- G-------------------------|-------2--0--------... D-----------0--2----------|-20----1-------4--2--... A--0--2--4----------0-----|-------4--2-----...----- E-------------------------|-------------4--...---- A B C# D E A D A G F# E
Notice how we end the key of A with a strong authentic cadence; but immediately use a phrase with DG instead of G{{s}}, which is to differentiate between the only note in E Major that isn't diatonic to keys of A and D Major. We also use an E in the first measure, but Em in the second. This emphasizes the modulation, with separation between phrases, even though the 2 keys share 6 of their 7 notes.
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For example, consider the following progression:
Cm B Bb Bbm A Ab Abm G Gb Ebm Abm Cm: i VII Bbm: i VII Abm: i VII VII v i E---8--11-10-6-----------6--9--8--4-----------4--7--6--2---------2--4-- B-------------------------------------------------------------4-------- G---------------------------------------------------------------------- D---------------------------------------------------------------------- A---------------------------------------------------------------------- E----------------------------------------------------------------------
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[[Modes#Pitch Axis Theory|Pitch Axis Theory]] (also see [http://en.wikipedia.org/wiki/Pitch_axis_theory Wikipedia]) is an extreme example of this. It uses chord progressions that all feature a common note - often this note is the root of every chord in the progression. The underlying chords are not diatonic to any one key. Instead, the scale used for melody/lead will change to conform with each chord.
A Am Adim A+
A: I Am: i Awh: io Awt: I+
E--0----------0---------------------1--
B--2----------1----------1----------2--
G--2----------2----------2----------2--
D--2----------2----------1----------3--
A--0----------0----------0----------0--
E--------------------------------------
Note, we have not covered [[Exotic Scales|exotic scales]], such as the whole-half or whote-tone scales yet, which are referenced above as "Awh" and "Awt".
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Modulation can be used for a variety of purposes. It is generally used as a means to add contrast to different sections or themes in a song. The altered tonality adds to the change in harmonic progressions or melody. It can highlight how much contrast between themes or sections there is depending on how related the chosen keys you modulate to/from.
Just as an ascending melody can be used to build excitement, modulating keys higher and higher can be used the same way. The frequency of modulations can also be used to indicate such - increasingly frequent modulations can make the piece sound a bit chaotic but also make things seem out-of-control with energy. The same can be done descending as a calming method. If the modulations follow an easily-identified pattern, such as in a rosalia, they will not sound chaotic but mellow - it allows repetition while still creating movement.
Modulations can also be used to make a piece sound disjointed, similar to playing in scales with an ambiguous tonality. Or they can allow the piece to use lots of harmonic and melodic repetition without becoming increasingly boring.
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== Related Lessons ==
* [[Voice Leading|Prev: Voice LeadingCircle of Fifths]]* [[Chromatic Chords|Next: Chromatic Non-Diatonic Chords]]* [[Modes]]* [[Exotic Scales]]
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